An O(n log n) algorithm for finding all repetitions in a string
Journal of Algorithms
Structural properties of the string statistics problem
Journal of Computer and System Sciences
Optimal parallel pattern matching in strings
Information and Control
Theoretical Computer Science
Two-dimensional periodicity and its applications
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
An Alphabet Independent Approach to Two-Dimensional Pattern Matching
SIAM Journal on Computing
An Optimal O(log log n)-Time Parallel Algorithm for Detecting all Squares in a String
SIAM Journal on Computing
Double sequences with complexity mn+11
Automatica (Journal of IFAC)
Fibonacci arrays and their two-dimensional repetitions
Theoretical Computer Science
On a conjecture on bidimensional words
Theoretical Computer Science
Plane digitization and related combinatorial problems
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Theoretical Computer Science
Hi-index | 0.00 |
Repetitive substructures in two-dimensional arrays emerge in speeding up searches and have been recently studied also independently in an attempt to parallel some of the classical derivations concerning repetitions in strings. The present paper focuses on repetitions in two dimensions that manifest themselves in form of two "tandem" occurrences of a same primitive rectangular pattern W where the two replicas touch each other with either one side or corner. Being primitive here means that W cannot be expressed in turn by repeated tiling of another array. The main result of the paper is an O(n3 logn) algorithm for detecting all "side-sharing" repetitions in an n × n array. This is optimal, based on bounds on the number of such repetitions established in previous work. With easy adaptations, these constructions lead to an equally optimal, O(n4) algorithm for repetitions of the second type.